Achievable secrecy in arbitrary erasure networks with feedback

We present achievability schemes for secure message transmission in the presence of a passive eavesdropper, over arbitrary networks, where each edge corresponds to an independent erasure channel and we have available public channel state feedback. Our schemes are efficiently described through linear programming formulations, that generalize the information flow linear programs to networks with security constraints; different sources of secrecy show up as parameters in our linear programs, and solving the optimization problem enables to select the optimal (in terms of rate) scheme that integrates them. As far as we know, these are the first linear programming formulations for secret message transmission over arbitrary networks with erasures and channel state feedback.